Question

If (x+2) and (x-2) are factors of ax^4+ 2x^3 -3x^2+bx-4 , then find the value of a+b.

Answer 1

I hope it helps☺️☺️☺️☺️

Answer 2

Answer:

Step-by-step explanation:given that,(x+2) and (x-2) is factor of polynomial ax^4+2x^3-3x^2 + bx-4

In case 1

X+2=0

X=-2

P (x)= ax^4 + 2x^3-3x^2+bx-4

P (-2) =a (-2)^4 + 2(-2)^3-3 (-2)^2+b

(-2)-4

= 16a - 16 - 12 -2b - 4 =0

= 16a -32 -2b =0

= 16a - 2b = 32

= 8 (8a - b)=32

= 8a-b=16__________1

In case 2

Take out the remainder The same polynomial by taking factor as (x-2)

It will result 8a +b =o _______2

Add 1 and 2

(8a+b)+(8a-b)= 16+0

8a + b + 8a- b =16

8a+8a = 16

16 (a) = 16

a = 1

Putting value of a in 2

8a +b= 0

8 (1) +b =0

8+b=0

b=-8

a+b = 1+(-8)

=1-8

=-7